# which major is best?

#### Eric Smith

I am an undergraduate freshman and I go to a semi-target university. I am trying to decide between a statistics and an applied math major. Unfortunately, I'm already behind in either curriculum so I don't have time to experiment each major.

I know that people say major doesn't matter that much as long as it's quantitative; however, I am really just wondering which of these majors has the best curriculum, and hence will prepare me best for a mfe and a job in quantitative finance?

Statistics:
-Calc 1,2,3
-Intro to Stats
-Intro to programming

-Intro to decision science - Introduction to basic concepts and techniques of decision-making and information management in business, economics, social and physical science. Topics include discrete optimization, discrete probability, networks, decision trees, games, Markov chains

-Deterministic Models in Operations Research - Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory

-Introduction to probability - Probability models for random experiments. Basic properties of probability measures. Conditional probability and independence. Discrete random variables: hypergeometric, binomial, geometric, negative binomial, and Poisson. Continuous random variables: uniform, exponential, Gaussian, Cauchy and gamma. Jointly distributed random variables. Definition and basic properties of expectations, variances, covariances and correlations. Basic inequalities for probabilities and expectations. Laws of large numbers and the central limit theorem

-Stochastic Models in Operation Research - Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems inventory, and reliability, with emphasis on systems modeling, design, and control

-Statistical methods I - The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test. Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data.

-Statistical methods II - The focus of this course is on analysis of time series data, that is, data recorded in time. The topics of the course include estimation and elimination of trend and seasonal components, stationary time series, ARMA models, spectral analysis, modeling and forecasting of time series. Some statistical software will be used throughout the course to demonstrate how to apply the techniques on real time series data

-Linear Algebra for Applications - Algebra of matrices with applications. Solution of linear systems by Gaussian elimination. The Gram-Schmidt procedure. Eigenvalues and eigenvectors.

Statistics Electives:
Computational Mathematics for Decision Sciences - Reviews basic mathematical and computational theory required for analyzing models that arise in operations research, management science, and other policy sciences. Solution techniques that integrate existing software into student-written computer programs will be emphasized

Mathematical Statistics - Derivation and analysis of point estimators using decision theory, including the methods of Bayes and minimax estimation, maximum likelihood, method of moments, and unbiased estimation. Confidence intervals. Hypothesis testing, including Bayesian methods, multiple hypotheses, the Neyman-Pearson Lemma, simple and composite hypotheses, likelihood ratio tests, Type I and Type II errors, power calculations. Uses of and relationships between the families of standard probability models, including the Normal, Gamma, Chi-Squared, Student's T, Uniform, Beta, Binomial, Negative Binomial, Poisson, Hypergeometric, and Cauchy distributions, as well as the Poisson Process and the Bernoulli Process

Introduction to numerical analysis - Iterative methods, interpolation, polynomial and spline approximations. Numerical differentiation and integration, solution of ODEs and PDEs.

Applied Math
-Calc 1,2,3
-Intro to programming
-Discrete Mathematics
-Linear Algebra and Differential equations

-Advanced Calculus 1 :
Real number system.
Continuity, uniform continuity, and differentiability of functions of one variable.
The Riemann integral in one variable.
Uniform convergence, infinite series, power series.

-Linear Algebra or Linear Algebra for applications

-Introduction to numerical analysis
Iterative methods, interpolation, polynomial and spline approximations.
Numerical differentiation and integration, solution of ODEs and PDEs.

-Computer Assisted Mathematical Problem Solving
Computer as a tool in solving a variety of mathematical problems.
Possible topics: roots of equations, solutions to differential equations, others.
Introduction to appropriate programming language. Emphasis on graphics.

-Mathematical Modeling
Models and numerical simulations, using differential equations, iterated maps, and probability.

These are most likely the classes I will be taking if I decide to do either a stats or applied math major. I will probably take a couple of programming classes as well.

Also, I plan on double majoring in finance (since my university has a very good b-school)

So.... based on the classes I provided, which would be a better route? Stats or applied math?

#### JDawg

People tend to look more favorably at math majors than statistics majors. For example: statistics graduate programs actually favor math majors to statistics majors. So based on that, I'd go with applied math. As to which will be more useful in terms of teaching you the material that'll help you the most in the real world, I don't know.

#### albo

Eric, I'm also an undergraduate student, and I was in the same exact situation during my first year in college. I decided to go with a double in Mathematics and Financial Economics. When I look back, I think I've made the right choice. A Math degree is more sophisticated than a Statistics degree, as stats represent only one aspect of math. I believe the math major will give you a more prestigious background, appropriate for doing research, as well as applied analysis, so I would suggest you go with a Math-Finance combo.

Also, I would like to say that you have to come up with your original ways of how to apply the knowledge that you get in your college classes. During my freshman year, I opened an account with Ameritrade and I started trading. It helped me in the long run. So find something that you're passionate about, and try to apply your skills to it.

Good luck. #### ValueSeeker

Very good, mathematics is important and econometrics is useful (indirectly) to understand how scenarios may play out. However, I am not trying to knock you Albo (I think you are building a good framework), but what would you actually know about finance if you just did financial econometrics/mathematics? Those skills aren't exactly finance skills, they are more used for trading strategies (and trust me, your rules based strats would not be materially different from a typical trader-most are actually average. I have built some of them for the top players in Asset MGT). Can you tell me everything about how a company will allocate credit risk? If someone cannot answer that, they are the problem in finance and that is exactly why we are in a "no income and no career" generation. You have got to be able to think, not replicate a textbook!

#### albo

Very good, mathematics is important and econometrics is useful (indirectly) to understand how scenarios may play out. However, I am not trying to knock you Albo (I think you are building a good framework), but what would you actually know about finance if you just did financial econometrics/mathematics? Those skills aren't exactly finance skills, they are more used for trading strategies (I have built some of them for the top players in Asset MGT). Can you tell me everything about how a company will allocate credit risk? If someone cannot answer that, they are the problem in finance and that is exactly why we are in a "no income and no career" generation. You have got to be able to think, not replicate a textbook!

ValueSeeker, I don't think I mentioned the study of Econometrics in what I wrote. Also, if you read my post carefully, you can see that I advised the kid to study Finance, which means that you and I are on the same boat. However, if you want to know my personal opinion, I think an undergraduate business degree is a huge waste of time, unless you are a Wharton student. And you are very wrong when you assume that math people don't know anything about Credit Risk, Capital Allocation, etc. The problem with this generation is actually the opposite of what you say. The real problem is people majoring in "Finance" that end up working in Customer Services, because they cannot do simple arithmetic. But on the other side, an education is what you make of it.

I respect your experience in Asset MGT, maybe you should take a look at my resume and refer it to someone, if possible. #### ValueSeeker

Albo, Financial Econometrics is ~econometrics. (I know there are huge differences, but the approach is identical). I am not making an assumption about a lot of people who are brilliant in math not knowing about the allocation of corporate risks (such as credit risks), I have met too many people who don't actually think about it but are able to tell you about skewnesses within complex security exposures but take "the obvious" for granted such as understanding how a business is just a combination of contracts. If you want to talk generation, I will make the stand now that I have seen many people fail and many people climb extremely high. I know the in and outs of our generation, and trust me, with the good and bad I have seen, you have some people who are too scientifically smart that they end up stupid in decision making and others who don't know what TVM stands for.

However, Albo, you mention a doorway of things I agree with but cannot get into on this thread.

#### Benjamin H

Vote for math! My recommended classes would be:

Math
calc 1,2,3
linear algebra
calc-based probability
real analysis
complex analysis
ode
pde
numerical analysis(maybe 2 courses, one for general and one for pde)
stochastic process
measure theory
functional analysis
measure-based probability

CS
c++ programming
data structures

STAT
statistical inference
linear regression
time series analysis

#### Andy Nguyen Best major for what? A career in finance? A flexibility to apply to more industry?
I would suggest not to pigeonhole yourself into a narrow spectrum of jobs. I think data analyst is interesting, promising and applicable for many with similar skill set as MFE.
Stats, probability, skill set to analyze huge dataset are something going to help you.

• Connor

#### DanM

##### Math Student
In regards to the claim that an applied math major is more favorable or sophisticated than a stats major, I have to disagree. It depends on the school and the program. At my school, the coursework for a stats major is much more rigorous than that of an applied math major - it is actually comparable to pure math in terms of rigor. I know several people in my upper level real analysis course that are stats major, and only one applied math major. Courses like Mathematical Statistics, Stochastic Processes, Combinatorial math, etc are also part of the curriculum - these courses are very rigorous and demanding.

#### tfors

I am more or less in the same boat as the OP.

My reasoning is that since finance is mostly about pricing uncertainty and often deals with massive amounts of data, a solid statistics/econometrics major (including math) is actually more applicable than applied math. Depending on what type of quant you want to be of course.

Don't know if my reasoning makes sense? Still have some months to find out.

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